Estimation of fractal signals using wavelets and filter banks

A filter bank design based on orthonormal wavelets and equipped with a multiscale Wiener filter was recently proposed for signal restoration and for signal smoothing of 1/f family of fractal signals corrupted by external noise. The conclusions obtained in these papers are based on the following simplificative hypotheses: (1) The wavelet transformation is a whitening filter, and (2) the approximation term of the wavelet expansion can be avoided when the number of octaves in the multiresolution analysis is large enough. In this paper, we show that the estimation of 1/f processes in noise can be improved avoiding these two hypotheses. Explicit expressions of the mean-square error are given, and numerical comparisons with previous results are shown     

Analyzing blood cell concentration as a stochastic process

The hemogram is a prime index of evolution and prognosis of a variety of severe pathological disorders. The concentration of circulating blood elements, taken as a parameter of the system dynamics, displays a remarkable temporal variability. This variability can be considered as the integrated result of all the multiple interactions involved in controlling processes of generation, lifetime, and remotion of circulating cells. Designing a model able to satisfactorily predict the evolution (i.e., range of future values) of a hemogram series would be of high medical relevance. This article reports on basic characteristics of normal hemogram variability, analyzed as a stochastic process, within the framework of a mathematically defined theoretical model, the fractional Brownian motion. These results are compared with those obtained by standard spectral analysis: the autocorrelation function and its Fourier transform. Time series corresponding to day-to-day records of the circulating blood cells concentration obtained from two healthy sheep over a period of 1024 days were used